Scattering of long waves around a circular island mounted on a conical shoal

Abstract

Scattering of simple harmonic long waves by a cylindrical island mounted on a conical shoal in an otherwise open sea of constant depth is solved analytically based on the shallow-water wave (long-wave) theory. The new analytical solution not only confirms some conclusions and conjectures previously drawn from purely numerical studies, such as those showing how the slope of the shoal affects the amplification of the ocean waves around the coastline of islands, but also provides another useful check for numerical model developers.